Suppose i want to compute a 95% highest density for a beta distribution
beta(a,b)

the two end points x1 and x2 shoudl satisfy the following two equations:

pbeta(x1,a,b)-pbeta(x2,a,b)=95%

dbeta(x1,a,b)=dbeta(x2,a,b)

Is there any fast way to compute x1 and x2 in R?

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